2 Answers
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If you're not getting regular punctures due to the thin-ness of the tire or the fabric of the tire is showing/damaged, you can keep the tires on (Sheldon). Unlike a car tire, a tubular tire just requires the tire portion to prevent the tube from getting cut up. And road tires should be smooth since you don't need tread.

A number of the Continental models actually have two small divets in them that you can use to gauge the wear level of the tire. If present, I use those. Otherwise I look for excessive numbers of deep cuts in the tire, or some of the tire fabric showing through through the rubber.